scholarly journals Economical factorized schemes for third-order pseudoparabolic equations

2021 ◽  
pp. 44-57
Author(s):  
Мурат Хамидбиевич Бештоков
Keyword(s):  
General Theory ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Third Order ◽  
The Third ◽  
Stability Of Difference Schemes ◽  
The Stability ◽  
Pseudoparabolic Equations

Изучены экономичные факторизованные схемы для псевдопараболических уравнений третьего порядка. На основе общей теории устойчивости разностных схем доказаны устойчивость и сходимость разностных схем. Economical factorized schemes for pseudo-parabolic equations of the third order are studied. On the basis of the general theory of stability of difference schemes, the stability and convergence of difference schemes are proved.

scholarly journals Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Parabolic Equation ◽  
Fractional Calculus ◽  
Numerical Solution ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Implicit Schemes ◽  
The Stability

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.

scholarly journals Stability of delay parabolic difference equations

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 995-1006 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Deniz Agirseven
Keyword(s):  
Parabolic Equations ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Unbounded Operators ◽  
Stability Of Difference Schemes ◽  
Fractional Spaces ◽  
The Stability ◽  
Delay Differential ◽  
Parabolic Difference

In the present paper, the stability of difference schemes for the approximate solution of the initial value problem for delay differential equations with unbounded operators acting on delay terms in an arbitrary Banach space is studied. Theorems on stability of these difference schemes in fractional spaces are established. In practice, the stability estimates in H?lder norms for the solutions of difference schemes for the approximate solutions of the mixed problems for delay parabolic equations are obtained.

The Maximum Principle and Some of Its Applications

2002 ◽  
Vol 2 (1) ◽  
pp. 50-91 ◽  
Author(s):  
Piotr Matus
Keyword(s):  
Maximum Principle ◽  
Order Approximation ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Finite Difference Schemes ◽  
The Maximum Principle ◽  
Stability Of Difference Schemes ◽  
Mixed Derivatives ◽  
The Subject ◽  
The Stability

AbstractThe subject of this paper is the maximum principle and its application for investigating the stability and convergence of finite difference schemes. To some extent, this is a survey of the works on constructing and investigating certain new classes of monotone difference schemes. In this connection the maximum principle for the derivatives discussed in this paper is of fundamental importance. It is used as a basis for proving the coefficient stability of difference schemes in Banach spaces and the monotonicity of economical schemes of full approximation. New results on unconditional stability of monotone difference schemes with weights, conservative explicit-implicit schemes (staggered schemes), monotone schemes of second-order approximation in arbitrary domains, and monotone difference schemes for multidimensional elliptic equations with mixed derivatives are given.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Equilibrium and Stability of a Three-Dimensional Toroidal MHD Configuration Near its Magnetic Axis

1976 ◽  
Vol 31 (11) ◽  
pp. 1277-1288 ◽  
Author(s):  
D. Lortz ◽  
J. Nührenberg
Keyword(s):  
Three Dimensional ◽  
Magnetic Axis ◽  
Stability Criteria ◽  
Sufficient Criterion ◽  
Third Order ◽  
Stagnation Points ◽  
The Third ◽  
Longitudinal Current ◽  
The Stability

Abstract The expansion of a three-dimensional toroidal magnetohydrostatic equilibrium around its magnetic axis is reconsidered. Equilibrium and stability plasma-β estimates are obtained in connection with a discussion of stagnation points occurring in the third-order flux surfaces. The stability criteria entering the β-estimates are: (i) a necessary criterion for localized disturbances, (ii) a new sufficient criterion for configurations without longitudinal current. Hamada coordinates are used to evaluate these criteria.

An Numeric Method on the Third Order Term of KDV Equation

2011 ◽  
Vol 135-136 ◽  
pp. 253-255
Author(s):  
Yi Min Tian
Keyword(s):  
Difference Scheme ◽  
Kdv Equation ◽  
Order Term ◽  
Boundary Value ◽  
Difference Schemes ◽  
Boundary Values ◽  
Implicit Difference Scheme ◽  
Third Order ◽  
The Third ◽  
Numeric Experiment

Numeric scheme and numeric result was in this paper. First, We proposes a kind of explicit - implicit difference scheme to solve the initial and boundary value questions of the third order term of KDV equation here,and so we can solve the problem that the additional boundary values must be given first for present difference schemes when we try to realize the calculation by then., second, numeric experiment results was given ay the end of this article.

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